Truth as primarily intellectual
If truth is anthropocentric in its ontology, and it functions in a pragmatic and utilitarian manner, then truth in se apart from its usefulness must be seen as mainly intellectual. Just like secular (i.e. no sacred) knowledge from the sciences and the arts, knowledge is just a collection of intellectual facts. Knowledge of God's Word refers to intellectual comprehension of God's truth as revealed in the Bible. While acknowledging that we are to love God with all our mind (Mt. 22:37), love of God with one's mind is seen in purely intellectual terms.
Now, this phenomenon is not of course unique to the New Calvinists. But sometimes there can be many paths leading to the same destination, and this is one of them. The only difference between the New Calvinists and anti-intellectuals is that the New Calvinists do place some premium on doctrine and deeper knowledge of God's Word. There is an emphasis on reading the Scriptures to know who God is, but for them studying the Bible is not enough. Rather, very much like the pietists, one studies the Bible intellectually, and then one pays heed to its truth devotionally either through a separate time of prayer or meditation.
The problem with this approach is that Scripture contains no such dichotomy. Nowhere in Scripture is God's Word treated as mere knowledge. God's Word is living and active (Heb. 4:12), and it has its perlocutionary effect in bringing about what God desires it to do (Is. 55:11). God speaks through His Word, and there is absolutely no such distinction between the two Greek words used for 'word,' λογος and ῥημα, here, contrary to some especially in the Word-faith circles [Gordon H. Clark, The Johannine Logos (Jefferson, Maryland: Trinity Foundation, 1972, 1989), 46-58]. Where the Scriptures are read and are heard and are proclaimed, there God is speaking, and He continues to speak now today though His Word.
There are of course two types of ectypal truth, sacred and common/ secular. Common truth are certainly intellectual in nature. But sacred truth or God's truth is spiritual first, then intellectual. In fact, there is no real bifurcation of the spiritual and intellectual in God's truth. What is intellectual is spiritual and what is spiritual is intellectual. People in the Old Testament encounter God, and they came to know Him and His laws and decrees and statues. When they know His laws and decrees and statutes, they faced the God of the Covenant who obliged them to keep it. People in the New Testament encounter God in the person of Jesus Christ, and Jesus' teachings were communicated to them. There are no (mediated) encounters apart from knowledge, and no knowledge apart from an encounter (mediated) with God.
If all truth is spiritual and intellectual, then all of God's truth is spiritual, including hard doctrines like reprobation. There should not be an aversion to proclaiming all truth, as long as they are taught and proclaimed truly.